Diode Laser Locked to an Ultrastable Cavity. Louis Marmet, Alan A. Madej, Member, IEEE, Klaus J. Siemsen,. John E. Bernard, Member, IEEE, and Bradley G.
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 46, NO. 2, APRIL 1997
Precision Frequency Measurement of the S –D Transition of Sr with a 674-nm Diode Laser Locked to an Ultrastable Cavity Louis Marmet, Alan A. Madej, Member, IEEE, Klaus J. Siemsen, John E. Bernard, Member, IEEE, and Bradley G. Whitford, Member, IEEE
Abstract—We have measured the frequency of the 5s 2 S1=2 –4d D5=2 clock transition of a single Sr ion confined in a Paul trap. A diode laser locked to an ultrastable Fabry–P´erot (F–P) cavity was used to probe the transition with a resolution of 3.5 kHz. The absolute frequency was determined from heterodyne measurements referenced to an iodine stabilized HeNe laser and a CO2 laser yielding a value for the S–D transition of (444 779 043 963 630) kHz. This work could lead to the development of a new optical frequency standard at 674 nm. 2
URRENT interest in optical frequency standards in the visible has encouraged the use of Sr , a very promising candidate for a reliable frequency standard. This ion has the advantage that it can be cooled and probed with an all solid state laser system ,  using a diode laser at 674 nm to probe the 5s S –4d D clock transition. In our experiment, a scan of the 0.4-Hz natural linewidth transition takes a few minutes to complete. The 674-nm laser must therefore have a narrow linewidth and a good stability over time periods reaching thousands of seconds to achieve good resolution. This paper describes how the 674 nm diode laser is locked to an ultra-stable Fabry–P´erot (F–P) cavity and the properties of this cavity are reported. The cavity was initially studied with a 633 nm HeNe laser locked to a TEM mode. By measuring the beat frequency of the locked HeNe laser against an I -stabilized HeNe laser standard, precise monitoring of the cavity length could be obtained. Once characterized, the cavity was used to frequency-stabilize a 674 nm diode laser using the Pound–Drever–Hall technique . The ultrastable diode laser was used to record spectra resulting in an improvement of the absolute heterodyne frequency measurement of the S–D transition in Sr . II. THE ULTRASTABLE CAVITY The central component of our laser stabilization system is a reference F–P cavity. This cavity must be as stable as possible since it serves as a secondary frequency reference Manuscript received June 20, 1996; revised October 1, 1996. The work of L. Marmet was performed during a Visiting Fellowship in Canadian Government Laboratories Award from the National Research Council. The authors are with the Institute for National Measurement Standards, National Research Council, Ottawa, Ont., K1A 0R6, Canada. Publisher Item Identifier S 0018-9456(97)02134-7.
during the time required for the frequency measurement of the clock transition. The cavity spacer is made entirely of ULE (Corning), a material which has a null thermal expansion . Mirrors with coefficient at a characteristic temperature m and a high reflectivity dielectric coating ( radii 99.973%)  are optically contacted to the ends of the spacer. cm cm and a The spacer has dimensions of cm 1 cm diameter hole centered on the long axis. Two additional holes (2 mm in diameter), drilled perpendicular to each other and perpendicular to the long axis of the ULE cavity provide a path for evacuating air and a passage to insert fine rods. The rod ends are positioned within 1.5 mm of the optical axis to increase the losses of higher optical modes while keeping the TEM mode amplitude unchanged. The free spectral range of the cavity is 597 MHz and its finesse, calculated from the decay time of a transmitted light pulse, is 12 000. The cavity is supported horizontally at the Airy points with four stainless steel screws mounted on an INVAR cradle. The cradle is suspended by four springs attached to the top of a vacuum chamber to provide effective isolation from vibrations. Seven pairs of permanent magnets attached to the cradle damp oscillations of the unit with a decay time constant of 10 s through eddy currents induced in the aluminum wall of the vacuum chamber. The magnets of each pair are oriented in opposite directions to minimize the effect of external varying magnetic fields that would cause forces on the cradle. The cavity vacuum chamber is evacuated to a pressure of Pa with an ion pump. A copper wire is uniformly coiled around the chamber exterior to provide heating for temperature stabilization (maximum variation of 50 K in 15 h). The vacuum chamber is thermally insulated from the surrounding air with a 25 mm thick layer of Styrofoam insulation, a temperature stabilized aluminum shield, a double layer of 1 cm thick felt and a final external wall made from a 1 cm thick aluminum plate. The felt and the external wall also provide additional isolation from vibrations. The diode laser and vacuum chamber assembly are mounted on an optical table floating on a pneumatic system. The entire system is enclosed in a concrete room within the lab that attenuates external airborne acoustic noise by 40 dB. Two optical fibers enter the vacuum chamber giving access to both ends of the cavity to monitor transmitted and reflected light. They are attached to the cradle on kinematic mounts
0018–9456/97$10.00 1997 Canadian Crown Copyright
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 46, NO. 2, APRIL 1997
for alignment with the cavity. An antireflection coated ball lens ( mm) matches the fiber output with the optical mode of the cavity. The frequency of a HeNe laser is locked to a ULE cavity resonance. The laser frequency is dithered with a modulation frequency kHz and peak-to-peak deviations of 50 kHz. An amplitude modulated signal detected at 1f at the output of the ULE cavity is used by a servo loop to stabilize the frequency of the HeNe laser. The beat between this laser and one of our I -stabilized HeNe standard lasers gives the frequency of the resonant TEM mode. At the critical temperature , the length of the cavity reaches a minimum and thus the frequency of the resonant mode reaches a maximum. By monitoring the frequency of the cavity mode as a function of temperature, the various parameters characterizing the ULE spacer were found. The temperature of the cavity follows the temperature of the vacuum chamber with a thermal lag time of 11 h. The temperature of the ultrastable cavity does not vary by more than 23 K in a typical frequency measurement period of 15 h. The differential coefficient of thermal expansion was estimated to be K and C. Assuming that the cavity is kept at a temperature as far as 0.05 K away from the actual , a 23 K change would result in a frequency shift of 1 Hz, which is negligible. After these measurements, the temperature of the chamber was maintained at . Fig. 1 shows measurements of the frequency of the cavity mode obtained with the HeNe/ULE laser (open squares) and the frequency of a diode laser locked to the ULE cavity (black squares) obtained by monitoring the beat between synthesized 445 THz radiation and the diode/ULE laser. More details are given below for the measurements at 445 THz. The data obtained with the HeNe/ULE laser were scaled to 445 THz by multiplying them by 0.939 120 902 51 ( ), the frequency ratio of the diode/ULE laser and the HeNe/ULE laser. The data is closely fitted over 326 days by a function which includes an exponential and a linear dependence on time: 444 779 452 658 kHz 4.58 kHz/day 1800 kHz 55 days). The data points are fitted to within 30 kHz, the variations coming mainly from the resettability errors of the lasers used in the measurement of the cavity mode frequency and from deviations of the cavity mode frequency from the function . The frequency drift is likely due to settling of the optically contacted mirrors (contacted on April 5, 1994). The average drift rate of the resonance mode, as determined by the derivative of the function , was below 0.055 Hz/s after July 29, 1996 (day 308). This is, to our knowledge, the smallest long term drift rate ever reported for such a cavity. III. DIODE LASER LOCK The 674 nm diode laser system is shown schematically in Fig. 2. The laser is stabilized in two stages. For the first stage, optical feedback narrowing is achieved by a small folded F-P cavity (free spectral range 750 MHz, finesse 50). This cavity is tuned with a piezo mounted mirror and the feedback phase is controlled by a dither-free method . This technique reduces the linewidth of the laser to 40 kHz (1 s observation
Fig. 1. Frequency of a ULE cavity mode as a function of time spent under vacuum. The function f (t) = 444 779 452 658 kHz + 4.58 kHz/day t 1800 kHz exp( t=55 days) is plotted. Opened squares: HeNe/ULE laser (scaled to 445 THz), black squares: diode/ULE laser.
Fig. 2. Frequency stabilization system at 445 THz. Also shown is the HeNe laser system used to monitor the ULE cavity length changes. APD: avalanche photodiode, FI: Faraday isolator, FR: Faraday rotator, PP: polarizing prism.
time of a beat between two similar systems). Slow tuning of the laser is achieved with temperature control of the diode and PZT control on the tunable cavity. For the second stage of stabilization, the diode laser is tuned to a resonant mode of the ULE cavity near the target frequency of the 5s–4d transition. It is locked to the ULE cavity using the Pound–Drever–Hall technique . An EOM provides phase modulation at 25 MHz such that the sideband power is half the carrier power. The light reflected from the cavity is detected with an avalanche photodiode. The signal from the photodiode is sent to a phase detector providing a correction signal which is applied to the PZT on the optical feedback cavity and to the laser injection current for fast frequency correction. The use of an optical fiber for coupling to the cavity has the advantage of maintaining optical alignment with the cavity
MARMET et al.: PRECISION FREQUENCY MEASUREMENT
when the laser source is not on the same support . Such a technique was implemented, with due care being taken to avoid introducing back-reflections which are detrimental to a good frequency lock. The reflections from the ends of the fiber and from the input mirror of the F-P cavity produce a constant offset on the correction signal, resulting in a frequency offset. To reduce this offset, the ends of the fiber were cut at an angle, antireflection coated, and the fiber was cut to 390.9 cm length. With this length, the 25 MHz modulation on the signal reflected at one end of the fiber is 180 out of phase with the modulation on the signal reflected at the other end. This cancels the offset on the demodulated signal. All these techniques taken together have reduced the background by a factor of 100 which is somewhat worse than expected. Backreflections from damage points inside the fiber are the likely cause of the discrepancy. The diode/ULE laser is frequency calibrated by beating its output with synthesized reference light at 445 THz . This synthesized radiation is obtained by difference-frequency mixing of radiation from a high power HeNe laser and a CO laser. The 474-THz HeNe laser is polarization stabilized and provides 0.5 mW. A frequency counter monitors the beat between the power HeNe laser and a HeNe/I laser standard, giving a frequency calibration of the HeNe laser. The CO laser operates on the 10 m R(0) transition, and is frequency stabilized on the saturated absorption dip of NH . It provides 1 W at (28 832 030 680 21) kHz. The frequency mixing in a AgGaS crystal produces 5 nW at 445 THz. A second counter measures the frequency of a microwave oscillator which is phase locked to the beat between the synthesized frequency and the 445 THz diode laser frequency. The frequency of the diode laser is calculated from the known frequencies of the CO laser and the HeNe/I laser. The spectral width of the beat between the synthesized radiation and the 674 nm diode laser radiation has a FWHM of 4 kHz (0.1 s observation time). This width reflects the contribution of the widths of the CO laser, the HeNe laser and the 674 nm diode laser. Also seen on the beat signal are a pedestal and small sidebands (at least 20 dB below the carrier) that vary in amplitude with different gain adjustments of the diode laser servo loop, indicating that they are produced by the diode for averaging laser. The Allan deviation of the beat is 10 times of 200 s. This gives an upper limit on the frequency stability of the 674 nm diode laser which is a factor two larger than our I -stabilized HeNe laser standard. Since the diode laser is locked to a fixed frequency of the ULE cavity mode, the laser frequency must be shifted to reach the clock frequency of the ion. Tuning of the 445 THz laser frequency is achieved with an acousto-optic modulator (AOM) driven by a signal generator at 204 MHz. The beam is doublepassed through the AOM, providing the required 408 MHz to shift the frequency down to the 5s S –4d D transition frequency. The beam is sent through a fiber delivering 30 W to the Sr ion trap. IV. Sr ION EXPERIMENTS The experimental system used for ion trapping is described in detail elsewhere . The ion is confined in an rf Paul trap
with the characteristic dimension mm. It operates at 10 MHz with a drive voltage of 180 V. An oven filled with the Sr provides the source of atoms and electrons that ionize some Sr atoms. Once fluorescence at 422 nm is seen, the oven is turned off. Presently an Ar-ion laser pumped dye laser operating at 422 nm is used for cooling and detection of the ion on the S – P transition. An optical fiber carries 4.2 mW to a variable attenuator used to reduce this power to 60 W for the trap. Light emitted from the ion is collected and imaged into a small aperture in front of a photon counting photomultiplier. With one ion fluorescing, the measured photon count rates are above 5000 s ; the background rate is below 100 s . Since the P state can also decay to the D state, optical pumping of the P – D transition is required to maintain cycling on the resonant S–P transition. This is provided by 150 W of 1092 nm radiation from a diode laser pumped Nd -doped fiber laser. The cooling beam is passed through a chopper running at 70 Hz. A second chopper, synchronized but 180 out of phase with respect to the first one modulates the 674 nm probe beam to alternate the cooling and probing cycles. Quantum jumps are observed as an interruption of the 422 nm fluorescence that occurs when the probe beam excites the ion into the D state. Spectra are built from the quantum-jump rate measured as a function of the probing frequency. The background magnetic field inside the trap was estimated to be 43 T from the observed Zeeman splitting of the S–P transition. It is caused by the earth’s magnetic field, the magnets of the nearby ion pumps and other magnetic objects in the building. Measurements with a gaussmeter show that the magnetic field does not vary by more than 0.6 T in 6 h. However, variations of up to 0.2 T within a few seconds have been observed when magnetized objects (e.g., door) were moved. Faster variations of the field at the line frequency (60 Hz) reach 0.2 T, and a small variation of 0.05 T is also seen at 32 kHz. All these fields can shift the lines by a few kilohertz and a broadening of about 1.5 kHz (for the components) is expected from the fast variations of the magnetic field. To study the Zeeman shift, the magnetic field can be changed using coils mounted around the trap.
V. RESULTS Spectra taken at 43 T showed resolved Zeeman components 242 kHz on either side of line center. The peaks were identified as the Zeeman components from the analysis of spectra taken with increasing magnetic fields. The components shifted by about 5.6 kHz/ T, the accuracy of this value being limited by our knowledge of the background magnetic field. The Zeeman component of the 5s S –4d D transition is shown in Fig. 3. It was taken with 1 kHz steps and 10 s averaging per channel. The error bars indicate the statistical error associated with the number of counts in each channel. Since large spectral regions have been scanned to study the properties of the trap and optimize its operating parameters, the number of counts for
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 46, NO. 2, APRIL 1997
the lock of the laser to the ULE cavity. These results compare favorably with the stability of our HeNe/I laser. VI. CONCLUSIONS
Fig. 3. Spectrum of the (mj ; mj ) = ( 1=2; 1=2) Zeeman component of the 5s 2 S1=2 –4d 2 D5=2 transition in Sr+ with best Lorentzian fit.
each particular line is limited. The uncertainty on the number of counts does not degrade the uncertainty on the position of the line to much more than the frequency step size. The line is fitted by a Lorentzian having 3.5 kHz FWHM, this width being the contributions of many broadening effects such as the probe laser linewidth and variations of the magnetic field. Other peaks of comparable amplitude appear in the spectra at regular intervals of 725 kHz measured from the Zeeman components. This frequency corresponds to the calculated radial secular frequency of the trap with the present operating parameters. These peaks are the motional sidebands of the components. With an increasing magnetic field, the peaks move in the same direction and at the same rate as the corresponding Zeeman component. Since the axial frequency is near twice the radial frequency, the sidebands at intervals of 1450 kHz nearly overlap the radial secular frequency sidebands. The series of motional sidebands extends to about 2 MHz away from line center. From the amplitude of these peaks, it is estimated that the temperature of the ion is 20 mK. The center frequency was calculated by averaging symmetrically located pairs of Zeeman lines that were measured in a single day. Based on values obtained on five different days the center frequency is (444 779 043 963 30) 5s S –4d D kHz (1 ). This value agrees with the most recent reported values , ; the uncertainty is at least an order of magintude lower than that given for the previous measurements. The five measurements show a sample deviation of 38 kHz, in agreement with the variations in the resettability of the CO laser (37 kHz) and of the HeNe/I laser (3 kHz), and on the estimation of line center (1 kHz) summed in quadrature. The estimated standard deviation of the mean is then 19 kHz to which the uncertainties of the laser standards must be added: 21 kHz for the CO NH laser and 12 kHz for the HeNe/I laser. The linewidth of the Zeeman components gives an upper limit to the laser stability of 3.5 kHz for a 50 s observation time, the time required for scanning the full width at half maximum of the line (see Fig. 3). Separate scans resulted in line positions not changing by more than 1 kHz after resetting
This absolute measurement of the 5s S –4d D transition was obtained by using heterodyne frequency measurements referenced to an I -stabilized HeNe laser and a CO NH laser. The value (444 779 043 963 30) kHz (1 ) was determined with an accuracy limited primarily by our knowledge of the frequency of the CO NH laser. The ULE cavity provided a highly stable frequency reference for the diode laser, not changing by more than 1 kHz relative to the ion transition over a period of many hours. It is very likely that the 445 THz laser can be frequency stabilized to the Sr ion to 1 kHz for 100 s averaging time, which is the time period required to scan the two Zeeman components. The ultra-stable diode laser tuned to the 5s–4d transition of Sr would then have a stability surpassing that of our HeNe/I laser, making it a candidate for a new frequency standard in the visible. Work to measure the absolute frequency of this transition directly against the Cs primary standard is now underway in this laboratory. REFERENCES  A. A. Madej and J. D. Sankey, “Single, trapped Sr+ atom: Laser cooling and quantum jumps by means of the 4d2 D5=2 –5s2 S1=2 transition,” Opt. Lett., vol. 15, pp. 634–636, June 1990.  G. P. Barwood, C. S. Edwards, P. Gill, H. A. Klein, and W. R. C. Rowley, “Observation of the 5s 2 S1=2 –4d 2 D5=2 transition in a single laser-cooled trapped Sr+ ion by using an all-solid-state system of lasers,” Opt. Lett., vol. 18, pp. 732–734, May 1993.  R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys., vol. B31, pp. 97–105, 1983.  A. A. Madej and K. J. Siemsen, “Absolute heterodyne frequency measurement of the 88 Sr+ 445 THz S–D single ion transition,” Opt. Lett., vol. 21, pp. 824–826, June 1996.  Mirrors from Particle Measuring Systems, Boulder, CO.  D. Schnier and A. A. Madej, “Dither-free method for phase-mirror control in optical-feedback stabilized diode laser systems,” Opt. Commun., vol. 105, pp. 388–396, 1994.  J. D. Sankey, “Coupling laser radiation to a Fabry-Perot Cavity with a single-mode optical fiber,” Appl. Phys., vol. B58, pp. 467–470, 1994.  G. P. Barwood, C. S. Edwards, P. Gill, G. Huang, H. A. Klein, and W. R. C. Rowley, “Precision interferometric frequency measurement of the 674 nm 2 S1=2 –2 D5=2 transition in a single cold Sr+ ion,” IEEE Trans. Instrum. Meas., vol. 44, pp. 117–119, Apr. 1995.
Louis Marmet was born in Qu´ebec City, P.Q., Canada, in 1962. He received the Ph.D. degree in physics from the University of Toronto, Toronto, Ont., Canada, in 1991. He worked on laser induced transparency at Lyman- and nonlinear processes in atomic hydrogen. In 1992, he joined the Max–Planck Institute for Quantum Optics, Garching, Germany, where he studied Rydberg wave packets in Rb atoms. He is currently with the National Research Council, Ottawa, Ont., Canada, working on laser stabilization for a frequency standard in the visible using the clock transition of Sr+ .
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Alan A. Madej (M’92) received the B.Sc. (Honors) degree from Acadia University, Wolfville, N.S., Canada, in 1983 and the M.Sc. and Doctoral degrees from the University of Toronto, Toronto, Ont., Canada, in 1985 and 1987, respectively. He is an Associate Research Officer with the Institute for National Measurements Standards, National Research Council of Canada, Ottawa, Ont., Canada, where he has worked since 1987 in the field of laser physics and trapped ion frequency standards. His work interests include frequency stablized laser systems, the use of ion traps for high-resolution spectroscopy, and the development of solid state laser sources for laser cooling, spectroscopy, and frequency stabilization. Dr. Madej is a member of the Optical Society of America and the Canadian Association of Physicists.
Klaus J. Siemsen was born in Berlin, Germany, on May 7, 1936. He received the Dr. Ing. degree from the Technical University, Berlin, in 1965. From 1966 to 1968, he was engaged in semiconductor research with the Noranda Research Centre, Pointe Claire, P.Q., Canada. Since 1968, he has been with the National Research Council of Canada, Ottawa, Ont. His research interests are in the experimental field of CW CO2 sequence lasers, pointcontact diodes, nonlinear crystals for laser frequency measurements, and optically pumped lasers.
John E. Bernard (M’89) was born in Weyburn, Sask., Canada, in 1955. He received the B.Sc. degree in physics from the University of Victoria, Victoria, B.C., Canada, in 1977 and the M.Sc. and Ph.D. degrees in plasma physics from the University of British Columbia, Vancouver, in 1979 and 1985, respectively. Since 1985 he has been with the National Research Council of Canada, Ottawa, Ont., where his research interests have been in the fields of laserplasma interactions, fiber sensors, diode-pumped solid-state lasers, and the development of lasers for spectroscopy and precision measurement. Dr. Bernard is Optical Society of America.
Bradley G. Whitford (S’58–M’58) was born in Manitoba, Canada, on November 8, 1934. He received the B.Sc. and M.Sc. degrees in electrical engineering from the University of Manitoba, Winnipeg, in 1958 and 1960, respectively, and the Ph.D. degree for work in microwave optics and antennas from McGill University, Montreal, P.Q., Canada, in 1967. From 1960 to 1963 he was with the Radio and Electrical Engineering Division, National Research Council of Canada (NRC), Ottawa, Ont., engaged in research on microwave components and techniques. He continued pursuits in the general field of microwave and optical diffraction at NRC until 1972 when he joined the Optical Physics Section and became occupied with absolute optical frequency measurements, and built a chain for linking the cesium standard frequency to infrared laser frequencies. He is currently the Frequency and Time Group Leader, Institute of National Measurement Standards, NRC, where he continues research to extend optical frequency measurements to the visible and to develop new optical frequency/wavelength standards.